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Interval valued picture fuzzy matrix: basic properties and application

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Abstract

The use of matrix theory in decision-making problems has been a subject of great interest for researchers. However, recent developments have shown that matrices can be enhanced by incorporating fuzzy, intuitionistic fuzzy, and picture-fuzzy theory. Inspired by the notion of interval-valued picture fuzzy sets (IVPFSs), we extend the idea of picture fuzzy matrix (PFM) into interval-valued picture fuzzy matrix (IVPFM) to represent more flexibly uncertain and vague information. The paper defines several key definitions and theorems for the IVPFM and presents a procedure for calculating its determinant and adjoint. Using composition functions, we develop algorithms to identify the greatest and least eigenvalue interval-valued picture fuzzy sets and use a flow chart to illustrate the procedure. The work demonstrates this process with a numerical example of a decision-making problem. In addition, we introduce a new distance measure for the IVPFSs and prove its validity with the help of basic properties. Further, the application of the proposed concepts has been shown by a real-life numerical example of a computer numerical controlled (CNC) programmer selection problem in a smart manufacturing company.

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  1. Department of Applied Mathematics, Delhi Technological University, New Delhi, 110042, India

    Vineet Kumar, Anjana Gupta & H. C. Taneja

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  1. Vineet Kumar
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Correspondence to Vineet Kumar.

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Kumar, V., Gupta, A. & Taneja, H.C. Interval valued picture fuzzy matrix: basic properties and application. Soft Comput (2023). https://doi.org/10.1007/s00500-023-09455-4

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